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A280991 Positive integers that can be expressed as the sum of four pairwise coprime squares.

%I A280991 #18 Jan 17 2017 02:35:40
%S A280991 3,4,7,12,15,19,27,28,31,36,39,43,51,52,55,60,63,67,75,76,79,84,87,91,
%T A280991 99,103,108,111,115,123,124,127,132,135,139,147,148,151,156,159,163,
%U A280991 171,172,175,180,183,187,195,196,199,204,207,211,219,220,223,228,231,235,243,244,247
%N A280991 Positive integers that can be expressed as the sum of four pairwise coprime squares.
%C A280991 If n is in the sequence, then n == 0 or 1 mod 3 and n == 3, 4, or 7 mod 8. But the converse is not true: 100 and 268 are not in the sequence (are there other examples?).
%C A280991 Guy [op. cit.] quotes Paul Turan as asking for a characterization of the terms of this sequence. - _N. J. A. Sloane_, Jan 16 2017
%D A280991 R. K. Guy, Unsolved Problems in Theory of Numbers, Section C20
%H A280991 Jean-François Alcover, <a href="/A280991/b280991.txt">Table of n, a(n) for n = 1..1000</a>
%e A280991 3 is in the sequence, since 3 is the sum of the squares of 0, 1, 1, 1 and these four numbers are pairwise coprime.
%e A280991 7 is in the sequence, since 7 is the sum of the squares of 1, 1, 1, 2 and these four numbers are pairwise coprime.
%t A280991 f[A_]:=Module[{A2, La2},A2=Subsets[A,{2}];La2=Length[A2];Union[Table[GCD@@A2[[i]],{i,1,La2}]]=={1}];
%t A280991 Select[Range[250],MemberQ[Union[f/@PowersRepresentations[#,4,2]],True]&]
%K A280991 nonn
%O A280991 1,1
%A A280991 _Emmanuel Vantieghem_, Jan 12 2017